Stimulated coherent Smith-Purcell radiation from a metallic grating

A relativistic electron beam with velocity v(b)(z) over cap passing over a metallic grating, with deep periodic depressions of wavenumber k(0)(z) over cap, excites a slow wave (omega, k(z)) via Cerenkov interaction, omega = ( k(2) + k(0))v(b). The beam bunches induce currents in the fins of the grati ng that act as a phased radiating dipole array, thereby generating coherent radiation at a wavelength lambda = (2 pi/k(0)l)(c/v(b) - sin theta) where l is an integer and theta is the angle of emission measured from the normal of the grating, The current threshold for the instability and radiation po wer scaling with beam current are discussed.